Training Numerical Intelligence via Auto-Diagnosis and Skill Discovery

arXiv cs.AIOctober 6, 2026en

arXiv:2610.03872v1 Announce Type: new Abstract: AI agents are becoming increasingly capable of generating scientific code, but generating code is not the same as improving the algorithms behind it. For numerical solvers, execution feedback can expose poor performance, but rarely reveals its underlying cause and how to address it. We introduce Auto-Diagnosis and Skill Discovery (ADSD), a framework that links numerical diagnosis to reusable solver self-improvement. ADSD follows a diagnosis-first paradigm that first explains why a solver performs poorly, then uses this diagnosis to guide the discovery of appropriate numerical methods. The resulting knowledge is packaged into reusable solver ski

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